Find the energy of an electron in the n = 4 state of hydrogen. ____eV If this el
ID: 1513079 • Letter: F
Question
Find the energy of an electron in the n = 4 state of hydrogen.____eV
If this electron undergoes a transition to the ground state, what is the energy, in electron-volts, of the photon that is emitted?
_____eV Find the energy of an electron in the n = 4 state of hydrogen.
____eV
If this electron undergoes a transition to the ground state, what is the energy, in electron-volts, of the photon that is emitted?
_____eV
____eV
If this electron undergoes a transition to the ground state, what is the energy, in electron-volts, of the photon that is emitted?
_____eV
Explanation / Answer
a)
here
E = h = hc / lambda
According to the Rydberg formula:
1/lambda = R(Z^2 / n^2) where
R = 1.097 x 10^7 m^-1
Z = Atomic number of the atom (Z=1 for hydrogen)
Combine these formulas:
E = hcR(Z^2 / n^2)
h = 6.626 x 10^-34 J·s
c = 3 x 10^8 m/sec
R = 1.097 x 10^7 m^-1
hcR = 6.626 x 10^-34 J·s x 3 x 10^8 m/sec x 1.097 x 10^7 m-1
hcR = 2.18 x 10^-18 J = 13.6 eV
E = 13.6 * (Z^2 / n^2)
E = 13.6 * 1^2 / 4^2 = 0.85 eV
b)
here also
E = 13.6 - 0.85 = 12.75 eV
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